Circuit-based Boolean Reasoning
Proceedings of the 38th annual Design Automation Conference
Combining strengths of circuit-based and CNF-based algorithms for a high-performance SAT solver
Proceedings of the 39th annual Design Automation Conference
Combining Decision Diagrams and SAT Procedures for Efficient Symbolic Model Checking
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Looking for an Analogue of Rice's Theorem in Circuit Complexity Theory
KGC '97 Proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory
Word problems requiring exponential time(Preliminary Report)
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Models and quantifier elimination for quantified Horn formulas
Discrete Applied Mathematics
Exploiting structure in an AIG based QBF solver
Proceedings of the Conference on Design, Automation and Test in Europe
Bounded model checking with QBF
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Rewriting (dependency-)quantified 2-CNF with arbitrary free literals into existential 2-HORN
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Exploiting circuit representations in QBF solving
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
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We consider the extension of Boolean circuits to quantified Boolean circuits by adding universal and existential quantifier nodes with semantics adopted from quantified Boolean formulas (QBF). The concept allows not only prenex representations of the form ∀x1∃x1...∀xn∃yn c where c is an ordinary Boolean circuit with inputs x1, ..., xn, y1, ..., yn. We also consider more general non-prenex normal forms with quantifiers inside the circuit as in non-prenex QBF, including circuits in which an input variable may occur both free and bound. We discuss the expressive power of these classes of circuits and establish polynomialtime equivalence-preserving transformations between many of them. Additional polynomial-time transformations show that various classes of quantified circuits have the same expressive power as quantified Boolean formulas and Boolean functions represented as finite sequences of nested definitions (NBF). In particular, universal quantification can be simulated efficiently by circuits containing only existential quantifiers if overlapping scopes of variables are allowed.